Details

sample231.0ms

Algorithm

intervals

Results

108.0ms	1451×	body	80	nan
32.0ms	397×	body	80	valid
9.0ms	21×	body	640	valid
4.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	1×	body	1280	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.5b	(log (- 1.0 z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
56×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`log-prod`
26×	`pow1`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

13.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
8.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series444.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
72.0ms	(* y (- (log z) t))
188.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify96.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune569.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Merged error: 0.0b

Counts

195 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
128×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-cube-cbrt`
80×	`times-frac`
74×	`associate-+r+` `associate-r`
71×	`distribute-rgt-in` `distribute-lft-in`
56×	`unpow-prod-down`
52×	`associate--l+`
34×	`associate-+l+`
33×	`pow1`
29×	`add-exp-log`
25×	`log-pow`
24×	`unpow2` `sqr-pow`
18×	`log-prod` `unswap-sqr`
14×	`distribute-lft-out--`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
9×	`div-exp` `add-log-exp`
8×	`sub-neg`
7×	`difference-of-squares`
6×	`pow-to-exp` `associate-l` `pow-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod` `cbrt-unprod`
2×	`pow-prod-down` `sum-log` `*-commutative` `rem-exp-log`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `exp-sum` `flip-+` `div-inv`

Counts

4 → 312

Calls

4 calls:

20.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
19.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
8.0ms	(* y (- (log z) t))
35.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
166.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
71.0ms	(* y (- (log z) t))
239.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify75.0ms

Algorithm

egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1481	4058
1	5001	3215

prune1.2s

Filtered

324 candidates to 197 candidates (60.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	323	1	324
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	325	3	328

Merged error: 0.0b

Counts

328 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
0.0b	(+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)
0.0b	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
0.1b	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `associate-l`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`exp-prod` `fma-def` `associate-r` `fma-udef` `distribute-lft-out`
2×	`associate-*l/` `log-pow`
1×	`+-commutative` `associate-+l+` `flip3--` `flip3-+` `exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `rem-exp-log` `difference-of-squares` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

9.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
3.0ms	(+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)
2.0ms	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
1.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series527.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
33.0ms	(+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)
180.0ms	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
231.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify99.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	292	924
1	899	829
2	4327	820
3	5001	819

prune344.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Merged error: 0.0b

Counts

84 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.5b	(log (- 1.0 z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
67×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
57×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`pow1` `log-prod`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
8×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`unpow-prod-down` `pow-unpow` `associate-l`
2×	`log-div` `pow-exp`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `e-exp-1` `pow-pow` `fma-def` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr` `sqr-pow`

Counts

4 → 188

Calls

4 calls:

6.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
8.0ms	(* y (- (log z) t))
17.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series450.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms	(* y (- (log z) t))
187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
48.0ms	(log (- 1.0 z))

simplify111.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	961	2008
1	3884	1597
2	5001	1582

prune580.0ms

Filtered

200 candidates to 130 candidates (65.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	199	4	203

Merged error: 0.0b

Counts

203 → 4

regimes303.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.1s	40261×	body	80	nan
991.0ms	12506×	body	80	valid
152.0ms	357×	body	640	valid
105.0ms	394×	body	320	valid
62.0ms	75×	body	1280	valid
42.0ms	253×	body	160	valid